testing “market beating” schemes and...
TRANSCRIPT
TESTING“MARKETBEATING”SCHEMESANDSTRATEGIES
2
TestingMarketEfficiency
• Testsofmarketefficiencylookatthewhetherspecificinvestmentstrategiesearnexcessreturns,afteradjustingforrisk.Sometestsalsoaccountfortransactionscostsandexecutionfeasibility.
• Atestofmarketefficiencyisajointtestofmarketefficiencyandtheefficacyofthemodelusedforexpectedreturns.Whenthereisevidenceofexcessreturnsinatestofmarketefficiency,itcanindicatethatmarketsareinefficientorthatthemodelusedtocomputeexpectedreturnsiswrongorboth.
3
Benchmarkstoassessperformance
¨ Comparisontoindices:Comparetoreturnsyouwouldhavemadebyinvestinginanindex,withoutadjustingforrisk.
¨ RiskandReturnModels:Youcanadjustforrisk,whenmakingyourcomparison:¤ MeanVarianceMeasures
n SharpeRatio:AverageReturn/StandarddeviationofReturnsfromStrategyn InformationRatio:(ReturnonStrategy– ReturnonIndex)/TrackingErrorversus
theIndex¤ CAPMbasedmeasures
n Jensen’salpha=Actualreturn– ExpectedReturn(fromCAPM)n TreynorIndex=(ReturnonStrategy– RiskfreeRate)/Beta
¤ ArbitragePricingandMulti-factorModels¤ ProxyandCompositeModels
4
Reviewingthechoices…
5
TestingEfficiency:Threeforms
¨ Inaneventstudy,weexaminewhethermarketsefficientlyincorporatethe”news”inanewsstory(earningsannouncement,acquisitionorevenaFederalReserveinterestratechange).
¨ Inaportfoliostudy,weexaminewhetherinvestinginangroupofassets/companiesthatsharethesamecharacteristic(lowPEratio,highdividendyieldsetc.)generateshigherreturnsthanitshould,giventheriskintheinvestments.
¨ Inaninvestorgroupstudy,weevaluatewhetheragroupofinvestorswhosharethesamecharacteristic(valueinvestors,hedgefunds,growth-orientedmutualfunds)beatthemarket,afteradjustingforriskandtransactionscosts.
6
1.EventStudy
• Aneventstudy isdesignedtoexaminemarketreactionsto,andexcessreturnsaroundspecificinformationevents.
• Theinformationeventscanbemarket-wide,suchasmacro-economicannouncements,orfirm-specific,suchasearningsordividendannouncements.
• Theobjectiveistoexaminewhethertheeventcausesstockpricestomoveabnormally(upordown).
7
Stepsinconductinganeventstudy
1. Specifythe“event”thatyouaretestinganddentifythe“time”theeventoccurred
2. Returnsarecollectedaroundthesedatesforeachofthefirmsinthesample.
a. Decideontimeintervals(hourly,daily,weekly)b. Determinehowmanyintervalsbeforeandafterevent.
3. Adjustthereturnsformarketperformanceandrisk,i.e.,estimateexcessorabnormalreturns.
4. Estimatetheaverageandstandarderrorinthesereturns.¤ Checkforstatisticalsignificance(Tstatistics,forexample)¤ Checkforeconomicsignificance(Areexcessreturnslarge
enoughtocoverexecutiondifficultiesandcosts?)
8
AnExample:TheEffectsofOptionListingonStockPrices
Step1:ThedateonwhichtheannouncementthatoptionswouldbelistedontheCBOEonaparticularstockwascollected.Step2:Thereturnsoftheunderlyingstock(j)werecomputedforthetendaysprior,thedayof,andeachofthetendaysafterannouncementStep3a:Thebetaforthestock(bj)wasestimatedusing100tradingdaysfrombeforetheeventand100tradingdaysaftertheevent.Thereturnsonthemarketindex(Rmt)werecomputedforeachofthe21tradingdays.Step3b:Excessreturnswerecomputedforeachofthetradingdays:
Erj,t =Rj,t - bj Rm,t .......... t=-10,-9,-8,....,+8,+9,+10Step4:Theaverageandstandarderrorofexcessreturnsacrossallstockswithoptionlistingswerecomputedforeach
9
TheResultsoftheStudy
10
2.PortfolioStudy
¨ Insomeinvestmentstrategies,firmswithspecificcharacteristicsareviewedasmorelikelytobeundervaluedorovervalued,andthereforehaveexcessreturns,thanfirmswithoutthesecharacteristics.¤ Inthesecases,thestrategiescanbetestedbycreatingportfoliosoffirmspossessingthesecharacteristicsatthebeginningofatimeperiod,andexaminingreturnsoverthetimeperiod.
¤ Toensurethattheseresultsarenotcoloredbytheidiosyncraticbehaviorofanyonetimeperiod,thisisrepeatedforanumberofperiods.
¨ Finally,tomakesurethatyourresultsarenottheresultofdatamining,youtryyourstrategyonaholdoutperiod.
11
StepsinDoingaPortfolioStudy
1. Thevariableonwhichfirmswillbeclassifiedisdefined,usingtheinvestmentstrategyasaguide.Thedataonthevariableiscollectedforeveryfirminthedefineduniverseatthestartofthetestingperiod,andfirmsareclassifiedintoportfoliosbaseduponthevariable.
2. Thereturnsarecollectedforeachfirmineachportfolioforthetestingperiod,andthereturnsforeachportfolioarecomputed.
3. The“risk”ofeachportfolioisestimated,usingoneoftheriskandreturnmodels.
4. Theexcessreturnsandstandarderrorsearnedbyeachportfolioarecomputed.
5. Usestatisticalteststoseeiftheexcessreturnsaredifferentfromzero.Theextremeportfolioscanbematchedagainsteachothertoseewhethertheyarestatisticallydifferent.
12
TestingalowPEstrategy
1. UsingdataonPEratiosfromtheendof1987,firmsontheNewYorkStockExchangewereclassifiedintofivegroups,thefirstgroupconsistingofstockswiththelowestPEratiosandthefifthgroupconsistingofstockswiththehighestPEratios.Firmswithnegativeprice-earningsratioswereignored.
2. Returnsoneachportfoliowerecomputedannually from1988to1992.Stocksthatwentbankruptorweredelistedwereassignedareturnof-100%.
3. Thebetasforeachstockineachportfoliowerecomputedusingmonthlyreturnsfrom1983to1987,andtheaveragebetaforeachportfoliowasestimated.Theportfolioswereassumedtobeequallyweighted.The returnsonthemarketindexwascomputedfrom1988to1992.
4. Theexcessreturnsoneachportfoliowerecomputedusingthebetasfromstep3andmarketreturnsfromstep4.
13
LowPEStrategy:ExcessReturns
P/E Class 1988 1989 1990 1991 1992 1988-1992Lowest 3.84% -0.83% 2.10% 6.68% 0.64% 2.61%2 1.75% 2.26% 0.19% 1.09% 1.13% 1.56%3 0.20% -3.15% -0.20% 0.17% 0.12% -0.59%4 -1.25% -0.94% -0.65% -1.99% -0.48% -1.15%Highest -1.74% -0.63% -1.44% -4.06% -1.25% -1.95%
Extreme portfolio testThe lowest PE portfolio earned 4.56% more than the highest PE portfolio. (2.61% - (-1.95%)) = 4.56%
Don’t forget your statistics. Every one of these numbers has a standard error attached to them and you can compute statistics (t, F) that will tell you whether these numbers are statistically significant.
14
Regressions
¨ Oneofthelimitationsofportfoliostudiesisthattheybecomeincreasingunwieldy,asthenumberofvariablesthatyouuseinyourstrategyincreases.
¨ Theotherproblemwithportfoliostudiesisthatyougroupfirmsintoclassesandignoredifferencesacrossfirmswithineachclass.Thus,thestocksinthelowestPEratioclassmayhavePEratiosthatrangefromthe4to12.
¨ Ifyoubelievethatthesedifferencesmayaffecttheexpectedreturnsonyourstrategy,youcouldgetabettermeasureoftherelationshipbyrunningamultipleregression.Yourdependentvariablewouldbethereturnsonstocksandtheindependentvariableswouldincludethevariablesthatformyourstrategy.
15
Runningaregression
1. Independentvariable:Thisisthevariablethatyouaretryingtoexplain.Inmostinvestmentschemes,itwillbeameasureofthereturnyouwouldmakeontheinvestmentbutyouhavetodecidehowyouaregoingtomeasurereturns(totalorexcess)andhowoften(daily,weekly,quarterly).
2. Dependentvariables:Thesearethevariablesthatyouthinkwillhelpyoufind“better”investments.Iftheyarequantitative(PEratios),youareset.Iftheyarequalitative(goodmanagement),youhavetocomeupwithaquantitativemeasureofthevariableatthebeginningofeachperiod thatyouarecomputingreturns.
3. Linearitycheck:Runscatterplotsforeachvariableagainstindependentvariabletoseeifrelationshipislinearornot.
4. Runtheregression:Youcaneitherruncrosssectionalregressions(acrossfirms)ortimeseriesregressions(acrosstime)
5. Checkforstatisticalsignificance:ChecktheR-squaredfortheregressionandthetstatisticsforthecoefficients.
16
3.InvestorGroupStudies
¨ Inthesestudies,youfocusonaninvestorgroupthatsharesacommoncharacteristicandexaminewhetherthereturnsdeliveredbythatgrouparehigherthanwhattheyshouldhaveearnedonarisk-adjustedbasistobreakeven.
¨ Sincethereturnsreflectexecutiondifficultiesandtransactionscosts,thisisamoredifficulttestformarketstopasstobedeemed“efficient”.
¨ Ineffect,youareexaminingwhetherstatisticalproofofmarketinefficiencytranslatesintoeconomicinefficiency.
17
Stepsininvestorgroupstudies
1. Identifythegroup:Specifythecommoncharacteristicsofthegroup.Insomecases,thiswillbeeasierthanothers.
2. Avoidsurvivorbias:Sincetheworstoftheinvestorsinyourspecifiedgroupmayfail,youshouldlookatallinvestorsinthegroupduringtheperiodofyourassessment,notjustsurvivors.
3. Measureactualreturns:Iftheinvestmentsareinmarket-tradedassets,thiswillbeeasier.Ifnot,bewaryofself-reportedreturns.
4. Evaluaterisk:Lookatboththeriskoftheunderlyinginvestments,aswellasthevariabilityintotalreturnsreportedforportfolios.
5. Calculateexcessreturns:Convertriskmeasureintoexpectedreturns,andcomputeexcessreturnasactualreturnminusexpectedreturn.
18
Example:Hedgefunds
1. Identifythegroup:Hedgefunds.2. Avoidsurvivorbias:Lookatallhedgefundsthatwereopenfor
investmentonJanuary1,20143. Measureactualreturns:Computereturnsonthesefundsevery
yearfrom2014-2018.Ifafundfails,computethereturnstoinvestorsinthatfundduringthefailedyear.
4. Evaluaterisk:Measurethevariabilityinhedgefundreturnsovertime.IfyouareusingtheCAPMoramarket-basedmodel,computethecorrelation(andbeta)ofthesereturns,relativetoamarketindex.
5. Calculateexcessreturns:Convertriskmeasureintoexpectedreturnseachyearandcomputeexcessreturnsforeachfund,eachyear.Computestatisticstoseeiftheaverageexcessreturnacrossfundsisdifferentfromzero.
19
TheCardinalSinsinTestingStrategies
1. Using'anecdotalevidence’:Anecdotescanbetailoredtocometoanyconclusion.
2. Noholdoutperiods:Aninvestmentschemeshouldalwaysbetestedoutonatimeperioddifferentfromtheoneitisextractedfromoronauniversedifferentfromtheoneusedtoderivethescheme.
3. SamplingBiases:Ifyoursamplingisbiased,itcanprovideresultsthatarenottrueinthelargeruniverse.
4. Failuretocontrolformarketperformance:Whentheoverallmarketisdoingwell(badly),allstrategieslookgood(bad).
5. Failuretocontrolforrisk:Afailuretocontrolforriskleadstoabiastowardsacceptinghigh-riskinvestmentschemesandrejectinglow-riskinvestmentschemes.
6. Mistakingcorrelationforcausation:Statisticaltestsoftenpresentevidenceofcorrelation,ratherthancausation.
20
OtherSins
1.DataMining:Theeasyaccesstohugeamountsofdataisadouble-edgedsword.Whenyourelatestockreturnstohundredsofvariables,youareboundtofindsomethatseemtopredictreturns,simplybychance.2.SurvivororSurvivalBias:Ifyoustartwithaexistinguniverseofpubliclytradedcompaniesandworkbackthroughtime,youcreateabiassinceyoueliminatefirmsthatfailedduringtheperiod.Ifthetestedstrategyissusceptibletopickingfirmswithhighbankruptcyrisk,thismayleadtoanoverstatementofreturnsonthescheme.3.NotallowingforTransactionsCosts:Someinvestmentschemesaremoreexpensivethanothersbecauseoftransactionscosts- executionfees,bid-askspreadsandpriceimpact.4.Notallowingfordifficultiesinexecution:Somestrategieslookgoodonpaperbutaredifficulttoexecuteinpractice,eitherbecauseofimpedimentstotradingorbecausetradingcreatesapriceimpact.
21
Askeptic’sguidetoinvestmentstrategies
1. Cantheinvestmentstrategybetested?Canitbeimplemented?
2. Ifthestrategycanbetested,isthetestthathasbeendevisedafaironeofthestrategy?
3. Doesitpasstheeconomicsignificancetests?4. Hasitbeentriedbefore?Thereistruthtothesayingthatalmosteverythingthatismarketedasnewanddifferentininvestinghasbeentriedbefore,sometimessuccessfully,andsometimesnot.